Min–max time efficient inspection of ground vehicles by a UAV team

Abstract

We present a control design for N unmanned aerial vehicles (UAVs) tasked with an inspection of M ground moving vehicles. The location of each ground vehicle is known to each UAV, but the navigation and intent of each ground vehicle are unknown, therefore, this uncertainty has to be anticipated in each UAV’s navigation. We use the minimum time stochastic optimal control to navigate each UAV towards the inspection of each ground vehicle. Based on this control, we formulate assignments of ground vehicles to be inspected by UAVs as an optimization problem to inspect all ground vehicles in the minimum expected time. Accounting for ground vehicle uncertain trajectories, we update the optimal assignment by a Markov inequality rule. The rule prevents the possibility of indefinite updating of assignments without finishing the inspection of all vehicles. On the other hand, it updates an assignment if it leads to a statistically significant improvement of the inspection expected time. The presented approach is illustrated with numerical examples.